If the absolute maximum value of the function $f\left(x\right)=\left({\mathrm{x}}^2-2\mathrm{x}+7\right){\mathrm{e}}^{\left(4{\mathrm{x}}^3-12{\mathrm{x}}^2-180\mathrm{x}+31\right)}$in the interval [–3, 0] is $f\left(\alpha \right)$, then:

$f^{\mathrm{\prime }}\left(x\right)=e^{\left(4x^3-12x^2-180x+31\right)}\left(12\left(x^2-2x+7\right)(x+3)(x-5)+2(x-1)\right)$

for $x\in [-3,0]$

$\Rightarrow {\mathrm{f}}^{\mathrm{\prime }}\left(\mathrm{x}\right)<0$

f(x) is decreasing function on [–3,0] 
The absolute maximum value of the function f(x)  is at x = –3

$\Rightarrow \alpha =-3$